Steve Bruce’s Magpies will travel to face the winners of the replay between the Pilgrims - the lowest-ranked team left in the competition - and League One Rochdale.
Speaking after Monday’s draw at the Etihad Stadium, Boston manager Elliott said: “It’s the perfect draw.
“If we’d have been given a lower-ranked team it may have been harder to motivate everybody.
“Getting a Premier League team is brilliant, but it only puts extra importance on the Rochdale game.
“It’s a mouthwatering tie, but we’ve got to get there.”
Elliott, who attended the draw along with chairman David Newton, vice-chairman Neil Kempster and secretary Craig Singleton, said the mood in the camp was high after being rewarded with the possibility of meeting a top-flight side.
“You don’t get anything better than a draw against a Premier League side,” added Elliott, whose team is the only National League North and Lincolnshire club remaining.
“The lads are excited. But they’re fully aware they’ve still got a job to do.
“It’s a good tie for Rochdale as well. They’ll want to beat us, no doubt.”
A date is yet to be confirmed for the replay at York Street, following Sunday’s goalless draw at Spotland.
The winning side will host Newcastle on the weekend of January 3.